Average Error: 0.0 → 0.0
Time: 8.6s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right) + \frac{1}{x - 1} \cdot \frac{1}{x - 1}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right) + \frac{1}{x - 1} \cdot \frac{1}{x - 1}}
double f(double x) {
        double r106679 = 1.0;
        double r106680 = x;
        double r106681 = r106680 - r106679;
        double r106682 = r106679 / r106681;
        double r106683 = r106680 + r106679;
        double r106684 = r106680 / r106683;
        double r106685 = r106682 + r106684;
        return r106685;
}
↓
double f(double x) {
        double r106686 = 1.0;
        double r106687 = x;
        double r106688 = r106687 - r106686;
        double r106689 = r106686 / r106688;
        double r106690 = 3.0;
        double r106691 = pow(r106689, r106690);
        double r106692 = r106687 + r106686;
        double r106693 = r106687 / r106692;
        double r106694 = pow(r106693, r106690);
        double r106695 = r106691 + r106694;
        double r106696 = r106693 - r106689;
        double r106697 = r106693 * r106696;
        double r106698 = r106689 * r106689;
        double r106699 = r106697 + r106698;
        double r106700 = r106695 / r106699;
        return r106700;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{1}{x - 1} + \frac{x}{x + 1}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}}\]

  4. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}^{3}}}\]
  5. Using strategy rm

  6. Applied flip3-+0.0

    \[\leadsto \sqrt[3]{{\color{blue}{\left(\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\frac{1}{x - 1} \cdot \frac{1}{x - 1} + \left(\frac{x}{x + 1} \cdot \frac{x}{x + 1} - \frac{1}{x - 1} \cdot \frac{x}{x + 1}\right)}\right)}}^{3}}\]

  7. Simplified0.0

    \[\leadsto \sqrt[3]{{\left(\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\color{blue}{\frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right) + \frac{1}{x - 1} \cdot \frac{1}{x - 1}}}\right)}^{3}}\]

  8. Final simplification0.0

    \[\leadsto \frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right) + \frac{1}{x - 1} \cdot \frac{1}{x - 1}}\]

Reproduce

herbie shell --seed 2019297 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))